"In Science the authority embodied in the opinion of thousands is not worth a spark of reason in one man." - Galileo Galilei

Tuesday, July 22, 2008

Energy Conservation: It's Not Just a Good Idea, It's the Law

Michael Eades latest blog points us to a review of Gary Taubes' Good Calories, Bad Calories by Dr. George Bray. Gary Taubes was given the opportunity to respond, and as usual, pretty much brings the wood, from the standpoint of logical clarity and consistency. I haven't read Bray's review in detail, but skimming over it I have to wonder how carefully he read the book. Indeed, he seems to essentially agree with Taubes that fat storage is driven by hormonal factors as part of overall metabolic regulation, and gives some examples where obesity results from failures in these regulatory mechanisms (which we'll also explore in subsequent posts in the Energy Regulation series). Despite this apparent agreement, Bray spends about 13 pages simultaneously trying to disagree with Taubes. Smells like cognitive dissonance, at least from my cursory reading. Taubes reply does a nice job at cutting through the fog.

Bray (like many others) seems to interpret Taubes work as somehow implying a violation or misunderstanding of the First Law of Thermodynamics, which is sort of humorous considering Taubes has a degree in physics from Harvard. Physics students pretty much get these sort of fundamental laws beaten into them from day one. In addition to Bray's review, there was a lot of noise about the First Law of Thermodynamics in response to the recently reported study about low-carbohydrate vs. low-fat diets. Being a physicist, I find misapplication of the First Law thoroughly annoying, so let's dig into this topic a bit and hopefully raise the level of understanding.

Use of the term "First Law of Thermodynamics" is a bit of historical accident. Bray actually uses the term I prefer, "Law of Conservation of Mass and Energy". Actually, "Mass" is redundant, since mass is just another word for energy, so let's shorten that to the "Law of the Conservation of Energy". The statement of energy conservation is simple: in a closed system, the total quantity of energy does not change. Energy may change "forms", e.g. the stored electrical chemical energy of battery can be converted to a light. But the total amount remains unchanged. The field of thermodynamics was largely developed in the 19th century, before we knew about atoms and such. We now understand that energy conservation in "thermodynamic systems" (consisting of very large numbers of atoms) simply follows from the more general law of energy conservation for all physical systems.

Why is energy conservation a "law"? There are many "conservation laws" in physics, and they all arise because of symmetries. Mathematically, physicists model the world via equations of motion, which basically tell how the state of the system under study changes as a function of changes in time and space coordinates. A "coordinate" is just a numerical label for a point in space (or spacetime). Suppose we're doing an experiment inside of a cubical box, 1 meter on each side. We might pick a point in the box, say the bottom left front corner, to be the "origin", labeled as (0,0,0). The top right back corner is then (1, 1, 1) in meters.

But this choice is arbitrary. I could just as easily pick any other point as the origin, say the front left corner of the parking lot, and update all of my other coordinate values accordingly. This is called a "transformation". Similarly, I could move my experiment box from it's original location. In neither case would I expect the experiment to have a different outcome. That's a symmetry: I changed one thing (coordinate origin, location of box), but it did not change the physics occurring inside the box. In this case, we would say the laws of physics are symmetric with respect to position.

A given symmetry in the equations of motion implies that some physical quantity is conserved, i.e. cannot change in a closed system. Symmetry with respect to position implies the conservation of linear momentum. Suppose I turn the box and observe the same outcome. This rotational symmetry implies conservation of angular momentum. Now let's do the experiment today, come back tomorrow, and repeat. If we get the same result, we have a time translation symmetry, which implies the conservation of energy. So basically, the "Law of Energy Conservation" arises from the observed fact that all of the fundamental equations of motion in physics are invariant under time shifts. It doesn't matter whether you look now or later, the laws governing how systems evolve in space and time are unchanged. Note that this is not the same as saying that the state of the system doesn't change, just that the laws which predict how the system goes from one state to another are not affected by the passage of time (this doesn't have to be true, it is just observed to be so in all cases so far).

Now, the above discussion is a bit watered down. The mathematically rigorous version is "Noether's Theorem", and involves differential calculus and continuous transformations. One of the best physics books I've read is Lagrangian Interaction, by Noel Doughty. Very technical, but a highly illuminating read on the power of symmetry in understanding the universe. There are many other fascinating and powerful applications of symmetry as well, one of my favorites being in Probability Theory. But we'll visit that another time.

So, to review: The First Law of Thermodynamics is just another statement of the more general Law of Energy Conservation. Energy conservation in a closed system arises because the laws of physics do not change with time. If you were to ever observe an apparent violation of energy conservation, it must be either that you are not observing a closed system (haven't taken everything into account), or you've discovered new laws of physics. The former is far more likely than the latter. For example, suppose you put some water in a cup, stuck in a thermometer, and put the whole she-bang into the freezer. The temperature would drop as time passed, indicating that the average energy of the water is decreasing. But this does not imply violation of energy conservation. Were you to also measure the net heat output from the freezer, you'd find the missing energy.

Back to our original story. Bray makes the point "Over the period of about 100 years from 1787 to 1896, the Laws of Conservation of Matter and Energy were shown to apply to human beings, just as they do to animals." That's a no-brainer given what we've learned above, since humans and animals are physical systems, ultimately governed by the same physical laws as the subatomic particles which comprise these systems. They didn't know about atoms and Noether's Theorem in the 19th century, so the explicit study of energy conservation in living organisms is understandable. But now it's not even a point of discussion, so I don't know why Bray (and so many others) keep lecturing about it. As far as anyone can tell, energy conservation is built-in to the fabric of the universe. The core issue isn't violation of this law, it's whether your metabolic theory or experiment has done a complete accounting of all energy inputs and outputs.

Energy enters the body in the form of food. In healthy people, the only way it can leave the body is through physical exertion or heat. Energy may be used in the body to fuel other biological processes ("base metabolic rate"), or it can be stored in various chemical forms. Misinterpretations seem to arise because there is an assumption that base metabolic rate and heat output are independent of caloric intake, and further independent of macronutrient composition. If you assume that intake is independent of storage and output, you can draw some strange conclusions. The body has ways of regulating total input, storage, and output in an attempt to maintain energy balance in a healthy range. As such, the output side must be related to the input side, otherwise energy regulation would be doomed to failure.

Consider a simpler example: drinking water. When we're thirsty, we drink water. The signal for thirst is generated in the brain as a function of the detected water content in the body. Too low, you get thirsty. But when you drink some water, it takes time for the water to get absorbed into the blood and signal the brain. So we tend to drink more water than we actually need; that's probably also a good evolutionary strategy, sort of "better safe than sorry". The body then has mechanisms to get rid of the excess, mostly as urine. The amount of urine we produce is clearly correlated to the amount of water we drink. If water output were independent of water input, we'd be in constant danger of either dehydration or water poisoning, depending on availability of water. Like food in Western society (and increasingly elsewhere), water is abundantly available, yet people aren't dropping dead from over-hydration because the input, usage, and output are regulated by the body. Why should we expect any different for energy regulation?

Like I said earlier, if it appears that energy conservation is violated in an experiment, such as the recent low-carb vs. low-fat diet study, the most likely explanation is that the experimenters did not measure all of the energy output. They did estimate physical activity, but it's more difficult to measure heat output. Similarly, Taubes is not saying "calories don't count", but rather that you must consider all methods of energy output when discussing energy balance. Further, you must consider the physiological mechanisms that control energy input, storage, and output, because that tells you relationships amongst them. When you do this, you find not only that output correlated with input, but also that the macronutrient composition potentially affects input, storage, and output as well. Macronutrients not only affect energy balance but other physiologically important quantities. Blood sugar, for example, is tightly regulated. If it goes too high or too low, the body has problems. So we would expect a different biological response if we eat the same calories as sugar or as fat, and of course this is exactly what is observed. It should not be surprising that high-carbohydrate or high-fat diets have very different effects on metabolism. Violation of energy conservation is not required to explain the results, just that the system has different responses to different inputs, and that the caloric content of food is only one aspect that is detected and monitored by the body.

Bray actually seems to agree with this point: "The concept of energy imbalance as the basis for understanding obesity at one level does not preclude any of the influences that affect or modify food intake or energy expenditure, including the quantity and quality of food, toxins, genes, viruses, sleeping time, breast feeding, medications, etc. They are just the processes that modifyone or other component of the energy-balance system." I think the fundamental disagreement may be whether fat storage depends sensitively on the precise balance between energy intake and output, i.e. that storage is driven by eating even a little too much. But that implies a pronounced lack of robustness in the regulatory system, one which is not observed, any more than it is in regulating water balance.

Anyway, the next time someone tells you that low-carb diets can't work because they violate the First Law of Thermodynamics, you can reply with "Low-carbohydrate diets exhibit continuous symmetry under time translation transformations, hence do not violate conservation of energy." That ought to shut 'em up.

15 comments:

"I think the fundamental disagreement may be whether fat storage depends sensitively on the precise balance between energy intake and output, i.e. that storage is driven by eating even a little too much. But that implies a pronounced lack of robustness in the regulatory system, one which is not observed, any more than it is in regulating water balance."

But can the regulatory system be impaired in some way where it plays a part in fat accumulation? Or is it the hormones influencing the regulatory system? In hypertension is the regulatory system not regulating water balance properly?

Sorry if questions are lame as I admit some of your post I didn't understand.

Dave,Nice essay. Your statement "Energy enters the body in the form of food" made me wonder if energy enters any other way. Sunlight is obvious because it causes Vitamin D synthesis, the good stuff. Cell phones?

Hi Mel. I wondered the same thing. It seems like the contribution from other sources must be very minimal. About the only thing I can think of is the ambient temperature, in the sense that when it's warm, the body doesn't need to generate as much of it's own heat. I can't think of any way other than eating that we would get some source of energy that directly leads to energy molecules like ATP. Interesting question.

Impairment of the regulatory system is what I believe causes obesity (and probably a lot of other problems as well). There are so many checks and balances in place that I find it very hard to believe that in healthy people consumption of minor caloric excesses leads to obesity. Going back to the water example, it's like saying that drinking an extra teaspoon of water every day ultimately leads to water poisoning. Any organism whose survival was that sensitive to a common environmental influence probably wouldn't last very long.

Hormones are a key part of the regulatory system. If the hormone levels are out of wack, or if the signals are not being received from the hormones, then the system is broken. Hormones also activate genes, so genetic issues can also arise, where the hormonal signal does not cause the desired effect.

I don't the answer to your question about hypertension. Some hypertension can be caused by blood vessels being constricted. This can be caused by chronic stress: one of the effects of stress hormones is to constrict blood vessels and increase blood pressure. That's a good thing if you're being chased by a lion, not so much if you get cut off in traffic. Does anybody else know if/how hypertension could be caused by impairment of water regulation?

Ambient temperature. I hadn't thought of that although I've been following a blog about the weight loss benefits of cold showers, brown fat mobilization or something. They are refreshing but I need more experience, only two so far.

BTW, when I said "No lame questions here", I meant "There are no lame questions here." If you didn't understand something I wrote, that's my fault, please do ask about it. We all need to work together to make sure everyone has information relevant to health decisions, rather than continuing to rely on "expert opinion".

There once was a popular defence of eating ice cream in large quantities that "proved" that it provided a net loss of energy. You look at the nutritional label on your ice cream and find that it has, say, 250 Cal per 100 g serving. Then you say, well, I know that ice cream has a specific heat of about 1 cal/g-C plus I have to unfreeze it at about 540 cal/g. So to raise the ice cream from solid at -5 C to liquid in the body at +37 C requires about 582 cal/g or 5820 cal for our 100 g serving. Wow! a net loss of 5820 - 250 = 5570 cal. Let's all eat ice cream and lose weight!

The problem, of course, is that the big-C Calorie used in nutrition is actually a kilocalorie (1000 small-c calories), so the arithmetic wasn't quite right...

The point is that while heat transfer obviously contributes to overall energy balance, it is usually a small effect. The body has important mechanisms for preserving and shedding heat, but they're there mostly to keep your body temperature under control, and I doubt that they play a very significant role in overall energy balance. My suspicion is that the key mechanism for dealing with excess food energy beyond that that can reasonably be stored in the short term is very simple: you just excrete it. I don't know why most accounts leave out this important method of disposing of excess energy.

First, a quick correction: I slipped a decimal point and calculated for a 10 g serving rather than a 100 g serving! My apologies. The ice cream serving will provide 58.2 kcal of cooling—more, but still not a lot, and most of it comes from the phase transition.

As to how energy can be excreted, it seems to me that there must be upper limits on how much food can be processed and how much energy can be stored in the period that processed food is resident in the digestive tract. Therefore, if you binge-eat or feast to consume more than this limit, then the excess should just pass all the way through the intestines and exit in the feces. It's just not clear how much gets excreted this way.

Without having done much research into this, we know that Ca intake can result in lipids being bound in the intestines and ultimately excreted without ever being absorbed. Same for soluble fiber—it interferes with formation of bile salt micelles and the resorption of these lipids (as well as some fat soluble vitamins probably), and is supposed to be the mechanism by which fiber lowers serum cholesterol (since bile salts are a form of cholesterol).

The postprandial thermogenesis shows a measureable dietary effect, but it's only about 0.2° F, and that's not going to result in a lot of additional energy loss even if the temperature remains elevated for a couple of hours. In fact the authors also show a post-prandial increase in resting energy expenditure of about 8 kcal/hr, which would clearly be lost in the noise of food quantities consumed. The authors claim a cumulative excess loss of about 90 kcal/day, roughly equivalent to about one extra "serving" of something, and still not enough to explain the observed difference in weight loss in my opinion. In this paper, both diets were 59% carbohydrates—I suspect that much more dramatic weight loss would be observed on a low carb diet!

This is not to say that we don't believe there could be dietary effects on energy balance, but it's not clear that people are looking at all the relevant factors yet.

I've just come across your blog and I'm really enjoying the thorough way in which you pursue your quarry. I've been on a similar quest to yourself (although my background is in law). I could not accept the health messages we were being fed (pardon the pun) without examining the evidence. At the end of a 4 year quest I became convinced that evidence overwhelmingly supported a conclusion that fructose (and the strange loopholes in our metabolism relating to it) was directly responsible for much that troubles the modern health systems of western countries.

I was lucky enough to have Penguin agree that it was a story worth telling in print form and the book hit the streets this week. You can read more about it at www.sweetpoison.com.au Try to ignore the populist spin, it really does get down to brass tacks as you get into it. I would love any feedback you would care to give and I intend to stay tuned to your posts from now on.

One point: food in the digestive tract is technically not inside the body. So undigested food energy is a separate issue from how the body dumps or stores excess calories once they've entered the blood.